Stability of reducing subspaces

Reducing subspaces

Let T be a self-adjoint operator acting in a separable Hilbert space H. We establish a correspondence between the reducing subspaces of T that come from a spectral projection and the convex, norm-closed bands in the set of finite Borel measures on R. IfH is not separable, we still obtain a reducing subspace corresponding to each convex norm-closed band. These observations lead to a unified trea...

Reducing Subspaces on the Annulus

We study reducing subspaces for an analytic multiplication operator Mzn on the Bergman space L 2 a(Ar) of the annulus Ar, and we prove that Mzn has exactly 2 reducing subspaces. Furthermore, in contrast to what happens for the disk, the same is true for the Hardy space on the annulus. Finally, we extend the results to certain bilateral weighted shifts, and interpret the results in the context o...

On reducing and deflating subspaces of matrices

A multilinear approach based on Grassmann representatives and matrix compounds is presented for the identification of reducing pairs of subspaces that are common to two or more matrices. Similar methods are employed to characterize the deflating pairs of subspaces for a regular matrix pencil A+ sB, namely, pairs of subspaces (L,M) such that AL ⊆ M and BL ⊆ M.

Exponential Stability of Subspaces for Quantum Stochastic Master Equations

We study the stability of quantum pure states and, more generally, subspaces for stochastic dynamics that describe continuously–monitored systems. We show that the target subspace is almost surely invariant if and only if it is invariant for the average evolution, and that the same equivalence holds for the global asymptotic stability. Moreover, we prove that a strict linear Lyapunov function f...

Comment on frame's of subspaces